11 papers · 1 filter
Assouad-like dimensions of random Moran measures
Kathryn E. Hare, Franklin Mendivil
In this paper, we determine the almost sure values of the -dimensions of random measures supported on random Moran sets that satisfy a uniform separation condition. The -dime…
Riesz bases of exponentials and the Bohr topology
Carlos Cabrelli, Kathryn Hare, Ursula Molter
We provide a necessary and sufficient condition to ensure that a multi-tile of of positive measure (but not necessarily bounded) admits a structured Riesz basis of expone…
The -spectrum for a class of self-similar measures with overlap
Kathryn E. Hare, Kevin G. Hare, Wanchun Shen
It is known that the heuristic principle, referred to as the multifractal formalism, need not hold for self-similar measures with overlap, such as the -fold convolution of the C…
Measures with specified support and arbitrary Assouad dimensions
Kathryn E. Hare, Franklin Mendivil, Leandro Zuberman
We show that if the upper Assouad dimension of the compact set is positive, then given any there is a measure with support and upper Assou…
Almost sure Assouad-like Dimensions of Complementary sets
Ignacio García, Kathryn E. Hare, Franklin Mendivil
Given a non-negative, decreasing sequence with sum , we consider all the closed subsets of such that the lengths of their complementary open intervals are given by t…
Intermediate Assouad-like dimensions
Ignacio García, Kathryn Hare, Franklin Mendivil
We introduce and study bi-Lipschitz-invariant dimensions that range between the box and Assouad dimensions. The quasi-Assouad dimensions and -spectrum are other special examples…